Question 177383
Let s = the length of the side of the original square.
If you increase this by 8 cm (s+8) and square it ((s+8)*(s+8)) you get 169 sq.cm. So you can write:
{{{(s+8)^2 = 169}}} Square the left side.
{{{s^2+16s+64 = 169}}} Subtract 169 from both sides.
{{{s^2+16s-105 = 0}}} Factor this quadratic equation.
{{{(s-5)(s+21) = 0}}} Apply the zero product rule:
{{{s-5 = 0}}} or {{{s+2 = 0}}} which means that...
{{{s = 5}}} or {{{s = -21}}} Discard the negative solution as the length of the sides can only be positive.
{{{highlight(s = 5)}}}cm  This is the length of the side of the original square.
Check:
{{{(s+8)^2 = 169}}}
{{{5+8)^2 = 169}}}
{{{13^2 = 169}}}
{{{169 = 169}}} OK!